Analytical Study of Unsteady MHD Flow Over a Vertical Porous Plate with Exponentially Accelerating Velocity, Temperature, and Concentration in the Presence of Hall Current, Chemical Reaction, Heat Source, and Dufour Effect

The erratic(unsteady) magnetohydrodynamic (MHD) natural convection-based HMT circulation throughout vertically permeable plate, about an exponentially varying rate, temperature and concentration respectively in occurrence of Hall phenomenon current, chemical reaction, heat source and Dufour effect is numerically analysed by using the Crank–Nicolson technique, subject to the specified conditions. A graphic representation and discussion of how the governing factors affect the speed(velocity) profiles are provided. The findings demonstrate that while the magnetic parameter, chemical reaction, and Schmidt number drops velocity, Hall parameter, thermal Grashof number, mass Grashof number, and permeability increase it.

Crank Nicolson, Reaction, Schmidt, Permeability (Porous), Hall.

1. Ganesan Radha, Ayothi Selvaraj, Soundararajan Bhavani, and Periasamy Selvaraju. “Magneto Hydrodynamic Effects on Unsteady Free Convection Casson Fluid Flow Past on Parabolic Accelerated Vertical Plate with Thermal Diffusion.” Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 116, no. 1 (April 25, 2024): 184–200. https://doi.org/10.37934/arfmts.116.1.184200. [Google Scholar] [Crossref]

2. Ganesan Radha, Ayothi Selvaraj, Neel Armstrong Abraham, Sundar Rajan Deepa, Mani Lakshmi, Devi Lakshmikaanth “First Order Chemical Reaction Effects on Unsteady MHD Casson Fluid Flow Past on Parabolic Accelerated Vertical Plate with Uniform Mass Diffusion and Variable Temperature in the Presence of Thermal Radiation” Journal of Advanced Research in Fluid Mechanics and Thermal Sciences,133,2025,pp:24-36. [Google Scholar] [Crossref]

3. Jothi E , Selvaraj A , Dufour Effect On Mhd Flow Past An Exponentially Accelerated Vertical Plate Through Porous System With Variable Temperature And Mass Diffusion J. Math. Comput. Sci. 11 (2021), No. 5, 6205-6215. https://doi.org/10.28919/jmcs/6104. [Google Scholar] [Crossref]

4. Selvaraj, A., and E. Jothi. “Heat Source Impact on MHD and Radiation Absorption Fluid Flow Past an Exponentially Accelerated Vertical Plate with Exponentially Variable Temperature and Mass Diffusion through a Porous Medium.” Materials Today: Proceedings 46 (2021): 3490–94. https://doi.org/10.1016/j.matpr.2020.11.919. [Google Scholar] [Crossref]

5. Karthikeyan, S., A. Selvaraj, and M. Venkateswarlu. “Rotating Significance of Parabolical Movement Antique with an Appearance on Isothermal Vertical Plate by MHD.” Materials Today: Proceedings 51 (2022): 1120–23. https://doi.org/10.1016/j.matpr.2021.07.109. [Google Scholar] [Crossref]

6. Karthikeyan, S., and A. Selvaraj. “Uniform Mass Diffusion on Thermal Radiation with Rotation of Parabolic in Progress Vertical Plate Set MHD.” Materials Today: Proceedings 51 (2022): 1074–78. https://doi.org/10.1016/j.matpr.2021.07.098. [Google Scholar] [Crossref]

7. Dilip Jose S and Selvaraj A, Convective, heat and mass transfer effects of rotation on parabolic flow past an accelerated isothermal vertical plate in the presence of chemical reaction of first order, JP Journal of Heat and Mass Transfer 24(1) (2021), 191-206. & http://dx.doi.org/10.17654/HM024010191. [Google Scholar] [Crossref]

8. Kavitha S, Selvaraj A, Senthamilselvi S and Rajesh P, ‘A Parabolic Flow With MHD, The Dufour and Rotational Effects of Uniform Temperature and Mass Diffusion Through an Accelerating Vertical Plate in The Presence of Chemical Reaction ”’, Journal of Advanced Research in Fluid Mechanics and Thermal Sciences,vol.110,no.2,pp.192-205,2023. [Google Scholar] [Crossref]

9. Hetnarski, Richard B. "An algorithm for generating some inverse Laplace transforms of exponential form." Zeitschrift für angewandteMathematik und Physik ZAMP 26 (1975): 249-253. https://doi.org/10.1007/bf01591514. [Google Scholar] [Crossref]

10. Balamurugan, K., M. Selvarasu, and V. Gopikrishnan. “MHD Free Convection Flow Past a Vertical Porous Plate in a Slip Flow Regime with Radiation Chemical Reaction and Temperature Gradient Dependent Heat Source in Hetnarski, R. "On inverting the Laplace transforms connected with the error function." ApplicationesMathematicae 4, no. 7 (1964): 399-405. https://DOI:10.4064/am-7-4-399-405 . [Google Scholar] [Crossref]

11. Rajakumar, K.V.B., K.S. Balamurugan, M. Umasankara Reddy, and Ch. V. Ramana Murthy. “Radiation, Dissipation and Dufour Effects on MHD Free Convection Casson Fluid Flow through a Vertical Oscillatory Porous Plate with Ion-Slip Current.” International Journal of Heat and Technology 36, no. 2 (June 30, 2018): 494–508. https://doi.org/10.18280/ijht.360214. [Google Scholar] [Crossref]

12. V. B. Raja kumar, K., K. S. Balamurugan, Ch. V. Ramana Murthy, and N. Ranganath. “Viscous Dissipation and Dufour Effects on MHD Free convection flow through an Oscillatory Inclined Porous Plate with Hall and Ion-Slip Current.” International Journal of Engineering & Technology 7, no. 4.5 (September 22, 2018): 410. https://doi.org/10.14419/ijet.v7i4.5.20194. [Google Scholar] [Crossref]

13. Lakshmikaanth D, Selvaraj A , Selvaraju P and Dilip Jose S, Hall and Heat Source Effects of Flow Past a Parabolic Accelerated Isothermal Vertical Plate in The Presence Of Chemical Reaction And Radiation, JP Journal of Heat and Mass Transfer Vol 34,2023,105-126.3 https://doi.org/10.17654/0973576323035 . [Google Scholar] [Crossref]

14. Lakshmikaanth, D., Selvaraj, A., and Neel Armstrong, A. [Google Scholar] [Crossref]

15. “Heat Source Effects of Flow Past a Parabolic Accelerated Isothermal Vertical Plate in the Presence of Hall Current, Chemical Reaction, Rotation and Radiation.” [Google Scholar] [Crossref]

16. European Chemical Bulletin, 12(4), 2023, pp. 3354–3374. https://doi:10.48047/ecb/2023.12.4.226. [Google Scholar] [Crossref]

17. Lakshmikaanth, D., A. Selvaraj, and S. Bhavani. "Exploration of the Impacts of Hall Effect, Dufour Effect, and Heat Source on Parabolic Flow over an Infinite Vertical Plate in the Presence of Rotation, Chemical Reaction, and Radiation in a Porous Medium." CFD Letters 17, no. 1 (2025): 60-77. https://doi.org/10.37934/cfdl.17.1.6077. [Google Scholar] [Crossref]

18. Lakshmikaanth, D., Selvaraj, A., Selvaraju, P., Dilip Jose, S., and Velukumar, V. [Google Scholar] [Crossref]

19. “Hall and Heat Source Effects of Flow State on a Vertically Accelerating Plate in an Isothermal Environment Including Chemical Reactions, Rotation, Radiation and the Dufour Effect.”JP Journal of Heat and Mass Transfer, 37, 2024, pp. 491–520. https://doi.org/10.17654/0973576324034 . [Google Scholar] [Crossref]

20. D.Lakshmikaanth, M.Krishnakumari, “MHD flow Over a Rotating vertical porous plate with exponentially accelerated velocity, temperature and Mass in the presence of Hall Current and Heat Source” International Journal of Latest Technology in Engineering , Management & Applied Sciences, Volume XIV, Issue XI, November 2025, 1218-1228. https://doi.org/10.51583/IJLTEMAS.2025.1411000116 . [Google Scholar] [Crossref]

21. Lakshmikaanth, D. “Hall, Soret And Heat Source Effects Of Parabolic Flow Past An Infinite Vertical Plate In The Presence Of Rotation With Chemical Reaction And Radiation” International Journal of Current Science, Volume 14, Issue 1 March 2024, 967-968. [Google Scholar] [Crossref]

22. Dilip Jose, S., Selvaraj, K., Sudha, P.N., Geetha, P., and Lakshmikaanth, D. [Google Scholar] [Crossref]

23. “Heat and Mass Transfer Effects on Parabolic Flow Past an Accelerated Isothermal Vertical Plate in the Presence of Chemical Reaction and Hall Current.” [Google Scholar] [Crossref]

24. JP Journal of Heat and Mass Transfer, 35, 2023, pp. 55–74. https://doi.org/10.17654/0973576323042 [Google Scholar] [Crossref]

25. Dilip Jose Sebastian, Mercy Priya Veeramani, Buvaneswari Shanmugam, Selvaraj Kandhasamy, Balakumar Rajakrishnan, Selvaraj Ayothi and Lakshmikaanth, D. “Unraveling the Complexities of Thermal Radiation and Rotational Dynamics in Parabolic Flow: A Perspective.”JP Journal of Heat and Mass Transfer, 37, 2024, pp. 617–639. https://doi.org/10.17654/0973576324040 [Google Scholar] [Crossref]

26. P Ramesh, Dr. E J Lalithkumar, Dr. D.Lakshmikaanth . “Investigation into the combined influence of the Hall effect, Soret effect, and heat source, alongside thermal radiation, chemical reactions, and rotational forces, within a porous medium, under flow which is para-bolic past an infinite vertical plate.” Journal of Nonlinear Analysis and Optimization, ISSN 1906 – 9685 UGC Care Approved, Group I, Peer Reviewed Journal Vol 16 Issue 1 [Google Scholar] [Crossref]

27. S. Abirami , A. Selvaraj , A. Kavitha , D. Lakshmikaanth , G. Kuppuswami “Multiphysical analysis of the Hall and dufour effects on radiatively accelerated casson fluid flow past an inclined rotating porous plate with chemical reaction” Next Chemical Engineering” Volume 2 , 2026 100055. https://doi.org/10.1016/j.nxcen.2026.100055 [Google Scholar] [Crossref]